I have posted several polar projections of MER panoramas (and Apollo and Surveyor pans in other places). This is how I do it...
I use Photoshop... any recent version is OK.
The tool to use is Filter>Distort>polar coordinates.
polar coordinates can work both ways - rectangular coordinates to circular or back. In map terms it lets you go from a cylindrical projection to an azimuthal (polar) one... in fact I have frequently used this with maps (for instance, take the cylindrical map of Titan from the JPL Cassini website, crop the southern half, and turn it into a pole-centered view of the southern hemisphere...)
For these pans you do the following.
1. 'polar coordinates' turns a rectangle into an ellipse. If you want a circle you have to make the rectangle a square. So I begin by resampling the pan to a square shape.. a 5000 by 1000 pixel pan becomes a 3000 by 3000 square. I cut off any unwanted sky first.
2. 'polar coordinates' puts the top of the rectangle at the center of the circle. So rotate the pan 180 degrees.
3. Then press the button and see what happens! You get a pan with the same horizon foreshortening as the original but wrapped into a circle.
4. I prefer a more maplike geometry, so the foreshortened distant areas need to be expanded relative to the foreground. I find it easier to do it this way:
- in step 1, I begin by making the 5000 by 1000 pan tall and narrow, maybe 3000 (wide) by 8000 (high). Then I select everythig except the near-horizon area and use edit>transform>scale (in my version, layer>transform>scale in others) to shrink the height of the selection about 10% or 15%. I keep repeating that with progressively smaller selections until at the end I'm only selecting a narrow strip of foreground and shrinking that. The result: the pan is now stretched higher near the horizon, and compressed near the foreground. Try it - trial and error will get decent results quite soon. NOTE: you could do this with some calculated figures to get more accurate geometry, but I just guess.
- then that modified pan is adjusted to be 3000 by 3000 pixels... usually with a bit of white space included at the bottom.
- then on to step 3 and see how it looks.
Let's keep them coming!
Phil